Benoit Mandelbrot

Benoît B. Mandelbrot ( born November 20, 1924 in Warsaw, † October 14, 2010 in Cambridge, Massachusetts ) was a French- American mathematician.

Mandelbrot made ​​contributions to a wide range of mathematical problems, including theoretical physics, financial mathematics and chaos theory. But he was best known as the father of fractal geometry. He described the Mandelbrot set and coined the term " fractal ". Mandelbrot was itself strongly to the popularization of his work at when he wrote books and lectured that were intended for the general public.

Mandelbrot spent most of his career at IBM's Thomas J. Watson Research Center, where he held the position of IBM Fellow. Later he became Sterling Professor of Mathematics ( Mathematical Sciences ) at Yale University. He was also a research associate at the Pacific Northwest National Laboratory, the University of Lille I, the Institute for Advanced Study and the Centre national de la recherche scientifique. Mandelbrot lived until his death in the United States.

Early life

Mandelbrot was born in Poland in a Lithuanian- Jewish family with academic tradition. His mother was a doctor, his father clothier. As a boy, Mandelbrot was introduced by two uncles in mathematics, one of which, Szolem Mandelbrojt, taught mathematics at the Collège de France. In 1936 the family moved to Paris to escape the impending threat to the Nazis.

Mandelbrot attended until the outbreak of the Second World War, the Lycée Rolin in Paris. He earned a reputation as a mathematical giftedness by its ability to visualize objects as geometric problems. At a national test, he has served as the only student in France a computing task. According to his own statement, he did not even try to only calculate the complicated integral, but realized that the task was a circle formula based and transformed the coordinates to use the circle in the solution. His family fled the German occupation in Vichy France, after Tulle, where supported him the Rabbi of Brive- la- Gaillarde in his education. From 1945 to 1947, he studied engineering at the Ecole Polytechnique in Gaston Julia and Paul Lévy. He then completed a degree in aeronautics at the California Institute of Technology, from which he graduated in 1949 with a master.

After studying Mandelbrot returned to France and obtained his doctorate in 1952 at the University of Paris in mathematics. From 1949 to 1957 he was a research associate at the Centre national de la recherche scientifique. During this time, Mandelbrot spent a year at the Institute for Advanced Study in Princeton (New Jersey), where he was supported by John von Neumann. 1955 married Aliette Kagan Mandelbrot, moved to Geneva and then back to France with her. After a year at Université Lille Nord de France Mandelbrot came in 1958 in the research department at the Thomas J. Watson Research Center at IBM and was promoted in 1975 to IBM Fellow, an award that allowed him considerable freedom for his research.

Scientific career

From 1951 Mandelbrot published work on problems of mathematics, but also about problems of applied areas such as information theory, economics and fluid mechanics. He was increasingly convinced that a variety of problems in these areas of two key themes were determined, namely "fat tail" probability distributions and self-similar structures.

Mandelbrot found that price fluctuations on the financial markets can not be described by a normal distribution, but by a Lévy distribution, which theoretically has an infinite variance. For example, he showed that cotton prices followed since 1816 a Lévy distribution with the parameters would correspond to a Gaussian distribution while (see also alpha- stable distributions ). He also provided a possible explanation for the equity premium puzzle.

Mandelbrot applied these ideas in the field of cosmology. In 1974, he proposed a new explanation for Olbers' paradox of the dark night sky. He showed that the paradox can be avoided without recourse to the Big Bang theory, if one assumes a fractal distribution of stars in the universe, in analogy to the so-called Cantor dust.

1975 Mandelbrot coined the term fractal to describe such structures. He published these ideas in the book Les objets fractals, forme, hasard et dimension ( 1975; an English translation Fractals: Form, Chance and Dimension was published in 1977 ). Mandelbrot thus developed ideas of Czech geographer, demographer and statistician Jaromír Korčák on, which had this published in the article Deux types fondamentaux de distribution statistique (1938; German Two basic types of statistical distribution).

During his tenure as Visiting Professor of Mathematics at Harvard University in 1979 Mandelbrot began to study the fractal Julia sets that are invariant to certain transformations in the complex plane and which have been previously studied by Gaston Julia and Pierre Fatou. These quantities are generated by the iterative formula. Mandelbrot use computer plots of this quantity in order to investigate their topology depending on the complex parameter. He discovered the Mandelbrot set, which is named after him.

1982 Extended Mandelbrot his ideas and published them in his well -known book, The Fractal Geometry of Nature ( the German translation appeared in 1987 under the title The fractal geometry of nature). This influential book made Fractal of a wider audience and also brought many of the critics silenced, fractals had previously dismissed as a programming artifact.

Mandelbrot left IBM in 1987 after 35 years with the company, after IBM had decided to dissolve its department for basic research. He then worked in the math department at Yale University, where at the age of 75 years, he took his first permanent professorship in 1999. When he retired in 2005, he was Sterling Professor of Mathematics. His last employment occurred Mandelbrot 2005 as Battelle Fellow at the Pacific Northwest National Laboratory.

Its most recent publication on fractal mathematical structures on the financial Fractals and Finance received the Business Book Award of the Financial Times Germany.

Fractals and roughness in nature

Although Mandelbrot coined the term fractal, some of the objects shown in The Fractal Geometry of Nature were described earlier by mathematicians. Before Mandelbrot, they were however rather viewed as unnatural mathematical oddities. It was Mandelbrot's merit to apply the fractal geometry for the description of real objects whose " rough ", not be described by simple idealizations objects escaped hitherto the scientific investigation. He showed that all these objects have certain properties in common, such as self- similarity, scale invariance, and often a non-integer dimension. Examples of natural fractals are the shapes of mountains, coastlines and rivers, branches of plants, blood vessels and alveoli, the distribution of star clusters in galaxies, and the paths of Brownian motion. Fractal structures are also found in quantitative descriptions of human creativity and action, such as music, painting and architecture as well as in market prices. Mandelbrot was therefore of the view that fractals are much more amenable to the intuitive recognition as the artificially smoothed idealizations of traditional Euclidean geometry:

" Clouds are not spheres, mountains are not cones, coastlines are not circles. The bark is not smooth - and the flash does not just make his way ".

Mandelbrot has been called a visionary and an independent spirit (English " Maverick "). Its generally understandable and passionate writing style and his emphasis figurative geometric intuition made ​​particularly his book The Fractal Geometry of Nature accessible to non-scientists. The book sparked a broad public interest in fractals and chaos theory.


Mandelbrot died at the age of 85 from pancreatic cancer. The mathematician Heinz- Otto Peitgen designated Mandelbrot on the occasion of his death as one of the most important personalities of the last 50 years for mathematics and its application in natural science. French President Nicolas Sarkozy praised Mandelbrot as a great and original mind whose work was completely beyond the scientific mainstream. The Economist also pointed out that his fame beyond science and called him the father of fractal geometry.

Selection of honors

1990 Mandelbrot was admitted as a Knight in the French Legion of Honor and promoted to officer in 2006. 2000, the small asteroid ( 27500 ) Mandelbrot was named after him. In May 2010 Mandelbrot received an honorary doctorate from the Johns Hopkins University awarded.


  • Richard Hudson fractals and Finance: Markets between risk, return and ruin, Piper 2007 (English original: The ( mis) behavior of markets: a fractal view of risk, ruin and reward, Basic Books 2004)
  • The fractalist: memoir of a geometer, Pantheon Books 2012
  • Selecta, several volumes, Springer Verlag, 1997
  • The fractal geometry of nature, Birkhauser, 1987, 2001
  • Fractals: Form, Chance and Dimensioin, Freeman, San Francisco 1977
  • The fractal geometry of nature, Freeman 1983
  • Beautiful Chaos: My Miraculous Life [ autobiography ]. Piper Verlag, 2013. ISBN 978-3-492-96162-2